According to the survey, however, far fewer Romanians and Bulgarians would actually end up coming to the UK.

The poll found that seven in ten of the Romanians who are thinking about moving to live in Britain would reconsider in the light of the restrictions to benefits being proposed by the Coalition.

The survey also said that of those saying they were considering coming to the UK, just 1.2 per cent of Bulgarians and 0.4 per cent of Romanians has indicated that they had started making concrete plans.

Large numbers also said they would only move to the UK if they had an offer of work from a UK company.

The survey found that when all of those polled were asked to pick their first choice of EU country to move to, 4.6 per cent of Romanians and 9.3 per cent of Bulgarians chose the UK.

According to a British Labour Force sample survey, there are currently 26,000 Bulgarians and 80,000 Romanians living in the UK.

Earlier this month study by the National Institute of Economic and Social Research (Niesr), a research group, found the number of Romanians and Bulgarians who will come to live in this country next year is “not possible to predict”.

However, it also signalled that Britain is woefully unprepared for the ending of migration restrictions at the end of this year.

The report suggested that any influx of Romanians and Bulgarians could put a strain on schools and be made worse by the economic crisis in Italy and Spain.

The Foreign Office insisted the report showed that there was “no reason at all to panic” about the lifting of the restrictions on Romanians and Bulgarians from December 31.

Niesr was asked by the Foreign Office to examine the “potential impact” of migration from Romania and Bulgaria, who joined the European Union on 1 January 2007. Despite being paid £30,000 of public money and drawing on more than 100 research works, Niesr was not explicitly asked to produce any estimates of how many people might come to the UK.

However the same think tank suggested in 2011 that around 21,000 immigrants from Romania and Bulgaria a year - substantially more than the 13,000 a year predicted in a report for the last Labour government - will come here.

Earlier this year Migration Watch, a thinktank which has a good record of forecasting migration, published figures suggesting that 50,000 a year Romanians and Bulgarians will come here, although others suggest this estimate is too high.

Philip Hollobone, Conservative MP for Kettering, said: “The reality is that nobody has any clear idea about how many people will come to the UK from Romania and Bulgaria.

“The BBC figures only have to be a little bit out for the numbers to be huge and significant. The British public feel hugely let down that the Government has not published any meaningful statistics on possible numbers.”